X-ray Tomography of One-forms with Partial Data
| Autor: | Keijo Mönkkönen, Joonas Ilmavirta |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Differential Geometry
46F12 44A12 58A10 Open set 01 natural sciences inversio-ongelmat integraaliyhtälöt Set (abstract data type) vector field tomography tomografia FOS: Mathematics Normal operator 0101 mathematics Mathematics x-ray tomography inverse problems Euclidean space Applied Mathematics Mathematical analysis Inverse problem unique continuation normal operator Functional Analysis (math.FA) Mathematics - Functional Analysis 010101 applied mathematics Computational Mathematics Differential Geometry (math.DG) röntgenkuvaus Tomography funktionaalianalyysi Analysis |
| Zdroj: | SIAM Journal on Mathematical Analysis. 53:3002-3015 |
| ISSN: | 1095-7154 0036-1410 |
| DOI: | 10.1137/20m1344779 |
| Popis: | If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the X-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions. Comment: 15 pages, 1 figure. Final version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|